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Linear completion

  • Hervé Devie
Chapter 3 Extension Of Knuth-Bendix Completion
Part of the Lecture Notes in Computer Science book series (LNCS, volume 516)

Abstract

We give an example of a set of linear equational axioms such that no finite canonical rewrite system can be computed by ordered completion with a complete reduction ordering, although such a rewrite system does trivially exist. We then describe a set of inference rules for a completion procedure, called linear completion, that solves the problem when the axioms are linear.

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References

  1. [1]
    L. Bachmair, “Proofs Methods for Equational Theories”, Thesis: University of Illinois at Urbana-Champaign, 1987.Google Scholar
  2. [2]
    L. Bachmair, N. Dershowitz and J. Hsiang, “Orderings for Equational Proofs”, Symposium on Logic in Computer Science, Boston, June 1986.Google Scholar
  3. [3]
    N. Dershowitz, “Personal Communication”, Montréal, June 1990.Google Scholar
  4. [4]
    N. Dershowitz and J.-P. Jouannaud, “Term Rewriting Systems”, in Handbook for Theoretical Computer Science, North-Holland, to appear.Google Scholar
  5. [5]
    N. Dershowitz and J.-P. Jouannaud, “Notations for Rewriting”, to appear Google Scholar
  6. [6]
    N. Dershowitz, L. Marcus and A. Tarlecki, “Existence, Uniqueness, and Construction of Rewrite Systems”, Technical Report.Google Scholar
  7. [7]
    J. Hsiang and M. Rusinowitch, “On Word Problems in Equational Theories”, 14th ICALP, 1987.Google Scholar
  8. [8]
    G. Huet, “Confluence Reductions: Abstract Properties and Applications to Term Rewritings, JACM, 27, 1980, pp. 797–821.Google Scholar
  9. [9]
    G. Huet, “A Complete Proof of Correctness of Knuth-Bendix Completion Algorithm”, JCSS, 23, 1981, pp.11–21.Google Scholar
  10. [10]
    G. Huet and D.C. Oppen, “Equations and Rewrite Rules: A Survey”, Formal Langages: Perspectives and Open Problems, R. Book, Academic Press, 1980.Google Scholar
  11. [11]
    D.E. Knuth and P.B. Bendix, “Simple Word Problems in Universal Algebra”, Computational Algebra, J. Leach, Pergamon Press, 1970, pp.263–297.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Hervé Devie
    • 1
  1. 1.LRI, Université Paris-Sud, Bât 490ORSAY CedexFrance

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